Physical Sciences and Mathematics Commons^™

On A Multistage Discrete Stochastic Optimization Problem With Stochastic Constraints And Nested Sampling, Thuy Anh Ta, Tien Mai, Fabian Bastin, Pierre L'Ecuyer

Research Collection School Of Computing and Information Systems

We consider a multistage stochastic discrete program in which constraints on any stage might involve expectations that cannot be computed easily and are approximated by simulation. We study a sample average approximation (SAA) approach that uses nested sampling, in which at each stage, a number of scenarios are examined and a number of simulation replications are performed for each scenario to estimate the next-stage constraints. This approach provides an approximate solution to the multistage problem. To establish the consistency of the SAA approach, we first consider a two-stage problem and show that in the second-stage problem, given a scenario, the …